Timothy Spall in Mr Turner: ‘Kisses a woman hungrily and clumsily, like a horse trying to eat a turnip’. Photograph: Allstar

The traditional poster shoutline is justified: Timothy Spall is JMW Turner! He is the triumphant star of Mike Leigh’s richly and intensely enjoyable study of the great artist’s final years. Turner looks like the pre-eminent Victorian: ruddy-cheeked, mutton-chopped, pop-eyed like a Toby jug or the figurehead on a ship’s prow. He is shown being lashed to a mast in a quasi-martyrdom of craft, with his sketchbook and pencils – the better to study and immerse himself in the drama and spectacle of a maritime scene. In Turner’s daily life, the great man harrumphs, snorts, growls and occasionally breaks groaningly into song. At work, he will spit at the canvas, mixing sputum with paint to create that challengingly hazy formlessness that outraged popular taste. This Turner will also kiss a woman hungrily and clumsily, like a horse trying to eat a turnip.

This is my second viewing since it was unveiled earlier this year at Cannes. Now it looks even more compelling: unhurried, discursive and mysterious. Spall’s performance shows an artist not encumbered with cliched bohemian torment, but one who is confident and prosperous, eccentric yet forthright, and self-assured in company. He briskly assesses the natural world for its physical properties and how these can be transformed and exploited for his purposes. This is a Turner with a good deal of Isambard Kingdom Brunel.

He lives the life of a bachelor, which means disregarding most of the women in his life and disavowing the resulting children and grandchildren because they get in the way of his work. Turner has an inconvenient ex-lover, Sarah Danby (Ruth Sheen), utterly unimpressed by his prestige, and he forces himself casually, almost absent-mindedly, on his submissive housekeeper Hannah (Dorothy Atkinson), who deteriorates into cronehood when she’s coolly thrown aside for the love of his life, widowed Margate landlady Sophia Booth – a lovely performance by Marion Bailey.

Since Mr Turner first appeared, the Late Turner exhibition at Tate Britain has established a new context for watching the film, encouraging us to see his later canvases as something other than proto-modernism, or a late Victorian variation on a Romantic theme. Their almost narcotic grandeur is Turner’s own: a transcendental refinement of the natural world, somehow existing in both the age of steam and the medieval world’s cloud of unknowing.

In Leigh’s film, Queen Victoria (Sinéad Matthews) dismissively puts this blurriness down to Turner’s fading eyesight. Quite unfair, although the film does return Turner to the vigorous, traditional Victorianism of character and narrative. Dick Pope’s cinematography is a deeply intelligent response to Turner’s canvases, but there is no loss of focus. It is as pin-sharp as both Leigh’s direction and the performances, and Gary Yershon’s delicate score creates the groundwork for its pathos. Like many critics, I have noted the cartoony, neo-Dickensian qualities of dialogue in Leigh’s films. Dickens isn’t mentioned here, although Turner sourly notes sharp-tongued Thackeray’s disapproval of his work.

What is also clearer on second viewing is the overwhelming importance of Turner’s deeply loved father, William Sr (Paul Jesson), a former barber who in his dotage is now Turner’s assistant. Like many a self-made man, Turner can see how much he has in common with his father and how easily he could have been exactly like him. William’s death scene is a heartbreaking premonition of Turner’s own; Leigh shows it as devastating and liberating, the end and beginning of an era. Turner has a kind of breakdown, tearfully visiting a brothel intending to paint one of the prostitutes, posing her in a theatrical attitude of despair. But then he is energised, finding a glorious new artistic purpose, and contentment with Mrs Booth.

Mr Turner is funny, humane and visually immaculate, hitting its confident stride straight away. It combines domestic intimacy with an epic sweep, and a lyrical gentleness pervades each scene, tragic or comic. Every line, every detail, every minor character, however casual or apparently superfluous, is absolutely necessary. When Turner is forced to attend a critical salon presided over by his great champion, the supercilious John Ruskin (Joshua McGuire), he endures a simperingly polite discussion of gooseberries. Every syllable of that is bizarrely riveting; it articulates Turner’s discomfiture and alienation. At such moments, Mike Leigh’s own artistry looks so commanding. With Vera Drake, Another Year and now Mr Turner, he’s produced three of his greatest films in the space of a decade. And there’s no sign of him letting up.